Learning Nonlinear Heterogeneity in Physical Kolmogorov-Arnold Networks

TL;DR

This paper introduces physical Kolmogorov-Arnold Networks (KAN) that train nonlinear synaptic elements, achieving higher performance with fewer resources compared to traditional linear-weight neural networks, demonstrated through silicon-based experiments.

Contribution

The paper presents the first experimental realization of physical KANs with reconfigurable nonlinear elements, showing superior task performance and resource efficiency over conventional networks.

Findings

Physical KANs outperform software neural networks in accuracy.

KAN devices operate efficiently at room temperature with minimal degradation.

Fewer parameters and devices are needed for comparable or better performance.

Abstract

Physical neural networks typically train linear synaptic weights while treating device nonlinearities as fixed. We show the opposite - by training the synaptic nonlinearity itself, as in Kolmogorov-Arnold Network (KAN) architectures, we yield markedly higher task performance per physical resource and improved performance-parameter scaling than conventional linear weight-based networks, demonstrating ability of KAN topologies to exploit reconfigurable nonlinear physical dynamics. We experimentally realise physical KANs in silicon-on-insulator devices we term 'Synaptic Nonlinear Elements' (SYNEs), operating at room temperature, microampere currents, 2 MHz speeds and ~750 fJ per nonlinear operation, with no observed degradation over 10^13 measurements and months-long timescales. We demonstrate nonlinear function regression, classification, and prediction of Li-Ion battery dynamics from noisy real-world multi-sensor data. Physical KANs outperform equivalently-parameterised software multilayer perceptron networks across all tasks, with up to two orders of magnitude fewer parameters, and two orders of magnitude fewer devices than linear weight based physical networks. These results establish learned physical nonlinearity as a hardware-native computational primitive for compact and efficient learning systems, and SYNE devices as effective substrates for heterogenous nonlinear computing.